#### THE

WESTERN INSTITUTE

FOR

ADVANCED STUDY

## GRAND CHALLENGES

Each year, we issue a new Grand Challenge in the field of mathematics, physics, or the biological sciences. We then devise a dedicated team of fellows who are highly motivated and well-equipped to pursue the research question. The results undergo a full peer-review process and then are made freely available to the public.

###### PREVIOUS AND ONGOING GRAND CHALLENGES

2018/2022: The physical basis of consciousness

A mechanistic explanation of consciousness has long proved elusive to philosophers and scientists. It is simply not understood what perceptual experience - the stream of thought - is, or how non-material mental states are produced by the operations of neural networks. The goal of this year's grand challenge is to devise a theory which provides a mechanistic framework for cognitive processes and a plausible physical explanation for thought. The 2018 effort successfully generated a theory which satisfies these requirements by combining the laws of neuroscience, information theory, and physics. This work came together with a follow-up effort in 2022 and is currently undergoing peer review.

2021/2023: Tackling computational complexity

The complexity of computational problems can be classified by the time resources required to identify a solution. Computational problems which can be solved in polynomial time by a deterministic Turing machine are classed as P. By contrast, NP problems can be verified in polynomial time but cannot be solved in polynomial time with deterministic computing methods. NP-hard problems include decision problems, search problems, and optimization problems which can be reduced in polynomial time from L to H, where H is a harder computation than L. NP-complete problems are problems which are both NP and NP-hard. The outstanding question is whether problems in this computational complexity class can be practically solved with non-deterministic computing methods. The 2021 effort is focused on studying what operational laws might guide non-deterministic computing at room temperature. The results of this initial effort are being compiled into a report; a follow-up effort will take place in 2023.

2020/2024: Living in an information-filled world

In the nineteenth century, Ludwig Boltzmann and Willard Gibbs determined the mathematical law for entropy, a quantifiable amount of disorder in thermodynamic systems. Later, Claude Shannon derived an astonishingly similar equation to measure information, the amount of disorder or non-compressibility in a dataset. Several years afterwards, John von Neumann extrapolated this equation into higher dimensions for use in quantum mechanics. Yet a functional link between these laws has remained out of reach, despite the common element of probabilistic mechanics which provides the foundation for thermodynamics, computing, and quantum theory. The grand challenge for 2020 is to address the following questions: How are information and entropy related? Do they play any significant role in the structure and operation of our universe? What are the implications of living in a probabilistic world, which generates information and entropy? The results of this initial effort are being compiled into a report; a follow-up effort will take place in 2024.

2019/2025: The emergent structure of the universe

A long-standing challenge in physics is reconciling quantum mechanics and general relativity. At quantum scales, a fundamental uncertainty in the position and momentum of a particle renders difficulty in measuring the curvature of space-time at its exact location. Meanwhile, at cosmological scales, the curvature of space-time appears irregular and dynamic. The goal of this year's grand challenge is to devise a theory which describes the curvature of the universe using force laws rather than empirically-derived constants which are not valid at every scale, and further to determine what this theoretical framework says about the earliest stages of the universe. The results of this initial effort are being compiled into a report; a follow-up effort will take place in 2025.